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Scientific Notation: Powers of Ten Rules for writing numbers in scientific notation: Write all significant figures but only the significant figures. Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below. a) Positive exponents push the decimal point to the right. The number becomes larger. It is multiplied by the power of 10. b) Negative exponents push the decimal point to the left. The number becomes smaller. It is divided by the power of 10. c) 10 o = 1 Examples: 3400 = 3.20 x = 1.20 x 10-2 Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!a view from outer space to the inside of an atom

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Errors Systematic Errors in a single direction (high or low) Can be corrected by proper calibration or running controls and blanks. Random Errors in any direction. Can’t be corrected. Can only be accounted for by using statistics.

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Standard Deviation The standard deviation, SD, is a precision estimate based on the area score: where x i is the i- th measurement x is the average measurement N is the number of measurements. y 0 x One standard deviation away from the mean in either direction on the horizontal axis (the red area on the graph) accounts for around 68 percent of the people in this group. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the people. Three standard deviations (the red, green and blue areas) account for about 99 percent of the people.

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Implied Range of Uncertainty Implied range of uncertainty in a measurement reported as 5 cm Implied range of uncertainty in a measurement reported as 5.0 cm. Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page Implied range of uncertainty in a measurement reported as 5.00 cm.

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20 10 ? 15 mL ? 15.0 mL1.50 x 10 1 mL

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Reading a Vernier A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up and down to measure a position on the scale. This could be part of a barometer which reads atmospheric pressure. The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in. If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale. 756

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Reading a Vernier A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up and down to measure a position on the scale. This could be part of a barometer which reads atmospheric pressure. The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in. If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale Scale Vernier

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If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately on the scale. If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is What is the reading now?

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If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately on the scale. If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is What is the reading now?

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Here is a final example, with the vernier at yet another position. The pointer points to a value that is obviously greater than and also less than Looking for divisions on the vernier that match a division on the scale, the 8 line matches fairly closely. So the reading is about In fact, the 8 line on the vernier appears to be a little bit above the corresponding line on the scale. The 8 line on the vernier is clearly somewhat below the corresponding line of the scale. So with sharp eyes one might report this reading as ± This "reading error" of ± 0.02 is probably the correct error of precision to specify for all measurements done with this apparatus

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Accuracy vs. Precision  Accuracy  Accuracy - how close a measurement is to the accepted value  Precision  Precision - how close a series of measurements are to each other ACCURATE = Correct PRECISE = Consistent Courtesy Christy Johannesson

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Reviewing Concepts Measurement Why do scientists use scientific notation? What system of units do scientists use for measurements? How does the precision of measurements affect the precision of scientific calculations? List the SI units for mass, length, and temperature.

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Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. a.Leading zeroes precede all the nonzero digits and DO NOT count as significant figures. Example: has ____ significant figures. b.Captive zeroes are zeroes between nonzero numbers. These always count as significant figures. Example: has ____ significant figures. c.Trailing zeroes are zeroes at the right end of the number. Trailing zeroes are only significant if the number contains a decimal point. Example: 1.00 x 10 2 has ____ significant figures. Trailing zeroes are not significant if the number does not contain a decimal point. Example: 100 has ____ significant figure. 3.Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53